Blackjack is all about representing numbers in your mind: How close am I to 21, and how likely is it that the next card will put me above that number? Can I take the risk of going “bust” by drawing another card? (The odds are reasonably easy to work out, and “cheat sheets” that summarize the statistics are available online. They likely do not come with a warranty.)

In their article, researchers Holmes, Ayzenberg, and Lourenco relied on previous evidence that mental arithmetic may involve dynamic shifts of attention, or simulated movement, along a left-to-right oriented mental “number line”. For example, when pointing to an arithmetic solution on a visually presented number line, participants are biased leftward on subtraction problems and rightward on addition problems. Similarly, when people must classify numbers by magnitude, responses are faster for smaller numbers if they involve response keys on the left, and likewise faster for larger numbers when the response key is on the right.

To examine whether a similar representation of numeric magnitude is used in Blackjack, Holmes and colleagues presented participants with a computerized version of blackjack in which successive playing cards were presented in the same central location on the screen. Participants pressed a central response key to obtain another card (“hit” in blackjack lingo) or withheld a response if they were satisfied with their current hand (called “stay” among professionals).

The main measure consisted of participants’ spontaneous eye movements on a blank screen following presentation of each card. Because all stimuli and the response key were located centrally, the task itself did not demand any eye movement or shift in attention. Accordingly, any relation between gaze patterns and hand value would be unlikely to reflect anything other than spatial-numerical mappings.

The figure below shows the events on a given trial:

To illustrate, suppose that people make use of the mental number line, with smaller numbers being represented on the left and larger numbers on the right. If a player were dealt a 2, followed by a 4, the total hand value (6) would be toward the lower end of the possible range of two-card hands (i.e., 4 to 21), and hence fixations might preferentially focus on the left side of the screen. By contrast, suppose a player was dealt a 10 and an 8, for a total of 18. In that case, the fixations might be focused more on the right of the screen.

The main result is shown in the figure below, which plots the horizontal offset from the center of eye movements during the blank period during which people presumably computed the updated total of their hand after the latest card has been presented.

The upward slope confirms that participants’ spontaneous eye movements along the horizontal axis reflected the overall numerical value of their cards. When the values in their hand were small, participants tended to look toward the left, and when the values were large they looked toward the right.

The figure also shows that these effects were driven by the total value of the hand and was not influenced by how many cards had been dealt: The blue line, which represents an early hand, has the same slope as the red line, which represents a later hand.

In a further analysis, Holmes and colleagues showed that the effect was not driven by the value of the last card being dealt—that is, the sequence 10-2-3 gave rise to the same set of eye movements as 2-3-10. This suggests that the eye movements do not reflect the magnitude of the last card being encoded but the result of the mental arithmetic required to sum up the hand across all cards.

So is there a “mental number line” and do we make use of it?

No single study can put that question to rest, but the results of Holmes and colleagues are quite suggestive of the use of spatial representations during mental arithmetic in a fairly complex task with a clear real-world analog.

Among the pros who author articles in poker magazines, eye movements have received attention because of their potential to reveal whether or not a player is bluffing. However, thus far, the idea of a number line does not appear to have found its way into the gambling community.

If the findings of Holmes and colleagues transfer from blackjack to poker, then perhaps an increasing number of poker players will resort to wearing sunglasses.